Question: Determine how many solutions exist for the system of equations. ${-6x-2y = 18}$ ${2x+y = -1}$
Explanation: Convert both equations to slope-intercept form: ${-6x-2y = 18}$ $-6x{+6x} - 2y = 18{+6x}$ $-2y = 18+6x$ $y = -9-3x$ ${y = -3x-9}$ ${2x+y = -1}$ $2x{-2x} + y = -1{-2x}$ $y = -1-2x$ ${y = -2x-1}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = -3x-9}$ ${y = -2x-1}$ The linear equations have different slopes. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ When two equations have different slopes, the lines will intersect once with one solution.